Semi-discretization of delayed dynamical systems

Proceedings of the ASME Design Engineering Technical Conference

Volumn 6 B, Issue , 2001, Pages 1227-1232

  Insperger, Tamás ^a   Stépán, Gábor ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DAMPING; LINEAR SYSTEMS; MATHEMATICAL MODELS; NUMERICAL METHODS; SYSTEM STABILITY; TIME VARYING SYSTEMS; DESIGN; DYNAMICAL SYSTEMS; TIME DELAY; VIBRATIONS (MECHANICAL);

DELAYED DYNAMICAL SYSTEMS; LINEAR DISCRETE SYSTEMS; LINEAR DYNAMICAL SYSTEMS; MATHIEU EQUATION; DELAYED MATHIEU EQUATION; DISCRETIZATIONS; EFFICIENT NUMERICAL METHOD; HIGH-DIMENSIONAL; SEMIDISCRETIZATION; STABILITY ANALYSIS; TIME-VARYING DELAYED SYSTEMS;

DYNAMICS; NUMERICAL METHODS;

EID: 0035790656     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (15)

1. Fargue, D., 1973, Réducibilité des systémes héréditaires á des systémes dinamiques, C. R. Acad. Sci. Paris 277B pp. 471-473.
2. Farkas, M., 1994, Periodic Motions, Springer-Verlag, New York.
3. Hale, J. K., Lunel, S. M. V., 1993, Introduction to Functional Differential Equations, Springer-Verlag, New York.
4. Hill, G. W. 1886, On the Part of the Motion of the Lunar Perigee which is a Function of the Mean Motions of the Sun and Moon, Acta Mathematica, 8, pp. 1-36.
5. Hsu, C. S., Bhatt, S. J., 1966, Stability Charts for Second-Order Dynamical Systems With Time Lag, Journal of Applied Mechanics, 33E(1), pp. 119-124.
6. Hurwitz, A., 1895, Über die Bedingungen unter welchem eine Gleichung nur Wurzeln mit negativen reellen Teilen besitz, Mathematische Annalen, 46, pp. 74-81.
7. Insperger, T., Stépán, G., 2000a, Stability chart for the delayed Mathieu equation, submitted to The Royal Society, Mathematical, Physical and Engineering Sciences.
8. Insperger T., Stépán, G., 2000b, Stability of the Milling Process, Periodica Polytechnica, 44, pp. 47-58.
9. Insperger and Stépán, 200c, Remote Control of Periodic Robot Motion, in Proceedings of 13th CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, Zakopane (2000), Springer, Wien, pp. 197-203.
10. Insperger, T., Stépán, G., Namachchivaya, S., 2001, Comparison of the dynamics of low immersion milling and cutting with varying spindle speed, in Proceedings of the ASME 2001 Design Engineering Technical Conferences, Pittsburgh, Pennsylvania, paper no. DETC2001/VIB21616 (CD-ROM).
11. Nayfeh, A. H., Mook, D. T., 1979, Nonlinear Oscillations, John Wiley and Sons, New York.
12. Routh, E., J., 1877, A treatise on the stability of a given state of motion, London.
13. Stépán, G., 1989, Retarded dynamical systems, Longman, Harlow.
14. Stépán, G., 2000, Vibrations of machines subjected to digital force control, International Journal of Solids and Structures, 38(10-13), pp. 2149-2159.
15. van der Pol, F., Strutt, M. J. O., 1928, On the stability of the solutions of Mathieu's Equation, Philosophical Magazine, and Journal of Science, 5, pp. 18-38.